No, bookmakers don't compute odds. They compute (and recompute) a number that will put 50% of the betting population on each side of the line. It has nothing to do with who is going to win.
That bookmakers try to split the betting money 50-50 might be true when the betting is against the spread. But not all betting is against the spread. It is also possible, for example, to bet on the "moneyline", i.e. on who is going to win the match. It is easy to see then that moneyline betting pays different odds for each team in match. In such cases the bookmaker, if he wants to guarantee a profit, has to split the money in a different way, for example if a team has 90% chance to win the match, he needs to take about 90% of the betting on that team. This is rarely possible though, because most betting happens on the favorites and when the favorites win the bookmakers mostly lose money.
You are also overlooking another component: That some bookmakers want to get the early action, and when they open the betting there is no line consensus to follow, so they have to set their own price. When this happens it means they *are* analyzing the matchup.
But even if we ignore all the aforementioned and only look at spread betting, where the 50-50 split is mostly possible, even then, it is not true to say that the betting odds have "nothing to do with who is going to win". They have *everything* to do with who is going to win. Peer-reviewed research has shown, time and time again (look at any of the papers here) , that betting markets are extremely efficient, i.e. betting odds reflect very closely the real probability of events. This happens *exactly* because the line is, to a large extent, shaped by public betting, which means that misconceptions on part of individual gamblers are cancelled out.